Gravity of an ancient Mars

Gravity is not dependent on the composition of the body. In fact, Jupiter exerts exactly the same gravitational influence that a solid body of the same mass would. So does the Sun, or a black hole.

The gravitational accelleration between two bodies for point masses can be simplified as $$g=-\frac{GM}{r^2}\hat{r}$$ where $G$ is the graviational constant, $M$ is the mass of the larger body, $r$ is the distance between the two masses and $\hat{r}$ is a unit vector directed from the large mass to the smaller mass. For our purposes, we can set $\hat{r}=1$ and ignore the minus sign, which reduces the formula to the perhaps better known $$g=\frac{GM}{r^2}$$

There is nothing in here that changes based on the type of matter making up $M$. Hence, for any given mass $M$ and a body with graviational constant $G$, the type of matter in $M$ makes no difference. We can therefore conclude that the gravitational accelleration on a Mars made up of any other material composition compared to our real, current-day Mars, but with the same total mass, would exert the same graviational influence on any surrounding bodies.

In the specific case of Mars, that is approximately $3.71{\text{ m/s}}^2$.

posted over 10 years ago

Canina‭

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